I've been using duckduckgo for searches on my phone and have been satisfied with it. I'll switch my home browser, too. What other near-zero effort things can I do? Does using a VPN offer privacy?
For phone, Firefox Focus and Brave are phone browsers with built-in tracking. Firefox Focus erases your browsing history automatically too. On the PC, Brave has built-in tracker blocking. Or use Firefox with plugins to block ads, trackers and unwanted scripts. Use the plugins UBlock Origin, Privacy Badger and HTTPS Everywhere. NoScript if you want to be hardcore but it's a pain because it breaks everything. A trustworthy VPN will protect you against two things: firstly, people eavesdropping on your traffic locally or at the ISP (though HTTPS and any other protocols with encryption ought to protect you against that too) and, secondly, authorities coming after your web browsing history, etc. Choose one that seems trustworthy, doesn't keep logs, and is based in a fictional lawless paradise. Good luck figuring out who fits the bill. (FWIW I have been using Nord VPN, which is quite cheap and easy to operate on both PC and phone.)
Definitely browser add-ons that deal with tracking cookies and the like, plus what galen suggested. I'd also recommend a plugin that obfuscates HTML canvas data, as that can be used to track you across websites. A VPN can offer a certain kind of privacy. It won't affect someone's ability to track you from one site to another (since that's based on creating a browser signature), but it does reduce the amount of eavesdropping that is possible. However, it really just means you're trusting the VPN provider not to spy on you as opposed to, say, your ISP.